G-Avoiding Sequence

You are given a set $S$ of distinct integers and an integer $G$. A sequence of integers is called a G-Avoiding Sequence if both of the following conditions hold:

1. the sequence is a permutation of the elements of $S$; and
2. for any two consecutive elements $A$ and $B$ in the sequence, $A - B$ is not divisible by $G$.

Compute the number of G-Avoiding Sequences modulo the prime 1,234,567,891.

The input consists of several test cases. The first line of each test case contains two integers $N$ ($1 \le N \le 200$), the size of $S$, and $G$ ($1 \le G \le 1000$). The next line contains $N$ integers, the elements of $S$, each between $0$ and $10^6$.

The input ends with a single line containing $N = G = 0$, which must not be processed.

For each test case, output a single line containing the number of G-Avoiding Sequences modulo 1,234,567,891.